Fundamentally, yes. Every material you see is made up of atoms, stuck together by chemical bonds. These bonds are not infinitely strong, so if you put in enough energy, you can break them, and the material will break up. It won’t necessarily melt in a way we are familiar with, but it won’t be solid any more.
So, the question is, can fires put out enough heat to break any chemical bond?
What we see as a fire is actually a chemical reaction. With a little encouragement, oxygen in the air bonds with whatever material is burning. The oxygen wants to do this so much that it gives off a lot of energy as it does so, and this is the heat that you feel from the fire. The temperature that a fire reaches is limited by how fast the oxygen can get into contact with the burning material.
An open, or unenclosed, fire might reach temperatures of around 1000°C, and a Bunsen burner flame, optimised to get as much oxygen to the fire as possible, can reach 1100°C. The absolute maximum temperatures achieved by a fire is around 2000°C, reached in blast furnaces and some welding techniques that attempt to provide absolute ideal conditions for a fire burning with oxygen.
The material tantalum hafnium carbide, on the other hand, is believed to have a melting point of 4215°C. We aren’t certain, because the only way to check would be to melt it, and it’s very difficult to reach such a high temperature for any reasonable quantity of material. But it’s clear that a block of this wouldn’t be melting in a fire any time soon!